The main contribution of this work is a stochastic Ho-Kalman Algorithm, where the standard SVD (which constitutes the main computational bottleneck of the algorithm) is replaced with an RSVD algorithm, which trades off accuracy and robustness for speed. We show that the stochastic Ho-Kalman Algorithm achieves the same robustness guarantees as its deterministic, non-asymptotic version in expectation. However, it outperforms the deterministic algorithm in terms of speed/computational complexity, which is measured by the total number of required floating-point operations (flops) [[1]}, §C.1.1]. Compared with \( O(pmn^3)\)  flops required by the deterministic algorithm, the stochastic Ho-Kalman Algorithm only requires \(O(pmn^2 \log {n})\)  flops.
